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research article

A Parareal Method for Time-fractional Differential Equations

Xu, Qinwu
•
Hesthaven, Jan S.  
•
Chen, Feng
2015
Journal of Computational Physics

In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global feature of fractional derivatives, the new method has in the correction step embraced the history part of the solution. We provide a convergence analysis under the assumption of Lipschitz stability conditions. We use a multi-domain spectral integrator to build the serial solvers and numerical results demonstrate the feasibility of the new approach and confirm the convergence analysis. Studies also show that both the coarse resolution and the nature of the differential operators can affect the performance.

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Type
research article
DOI
10.1016/j.jcp.2014.11.034
Web of Science ID

WOS:000354119500015

Author(s)
Xu, Qinwu
•
Hesthaven, Jan S.  
•
Chen, Feng
Date Issued

2015

Publisher

Elsevier

Published in
Journal of Computational Physics
Volume

293

Start page

173

End page

183

Subjects

fractional calculus

•

time-fractional

•

parareal

•

parallel-in-time

•

multi-domain spectral.

Peer reviewed

NON-REVIEWED

Written at

EPFL

EPFL units
MCSS  
Available on Infoscience
April 5, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/102542
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